# Aristotelian physics **Aristotelian physics** is the account of nature set out by [[Aristotle|Aristotle]] in the *Physics*, *On the Heavens*, *On Generation and Corruption* and *Meteorology*, in which [[Matter|matter]] below the [[Moon|Moon]] is compounded from four elements, each element moves of itself toward its natural place, and a body pushed through a medium moves at a speed fixed by the ratio of the mover's [[Force|force]] to the medium's resistance.[^phys-void] That rule is usually written v = F/R, and it is the part of the system the microsim tests. In the sim the reader sets the resistance constant k on a logarithmic scale and the body's mass, and watches the linear-drag equation m·dv/dt = m·g − k·v run: in honey and in air the body stops accelerating and settles onto Aristotle's line at v_T = m·g/k within about 2·v_T/g seconds, while in the void, where k → 0, it never settles and v = g·t runs away without limit. On the [[Physics|Physics]] flagship this article sits in Part I — History, at the section *Aristotle and Hellenistic physics* (row P3). Its argument is that Aristotelian physics is not a collection of errors but a theory of bodies in fluids, accurate in the regime where its authors worked and wrong precisely where they could not go.[^rovelli] The sim makes that concrete: v = F/R is the [[Terminal_velocity|terminal-velocity]] limit of the modern equation, and the void that Aristotle rejected on principle is the one place the limit does not exist. ## Methods Aristotle's physics is a science of causes stated in ordinary language, argued from what is evident to the senses and from the meanings of terms, and organised by definition and demonstration rather than by measurement. He gives no unit, no instrument and no table of data. Ratios appear — speeds are compared as "twice as fast", weights as "twice as heavy" — but the comparisons are qualitative proportions between whole situations, not numbers attached to quantities.[^phys-void] The [[Scientific_method|method]] is nonetheless empirical in its own way: the biological works rest on a body of dissection and observation that had no rival for two thousand years,[^bio] and the physical works appeal constantly to familiar behaviour — smoke rising, stones sinking, a cart stopping when the ox stops. Its weakness is not that it ignored the world but that it had no way to force a disagreement between a claim and the world into the open. [[Experimental_physics|Deliberate experiment]], in which a situation is built in order to make a theory fail, belongs to a later tradition. ## Concepts The system is tightly interlocked: the elements define the natural places, the natural places define natural motion, and everything that is not natural motion needs a mover in continuous contact. ### Elements and spheres Below the Moon there are four elements — earth, [[Water|water]], air and fire — generated from two pairs of contraries, hot/cold and wet/dry, so that each element can change into another when one contrary is replaced.[^gencorr] Above the Moon there is a fifth body, aether, which is ungenerated, unalterable and moves naturally in circles; the heavens are therefore made of different stuff and obey different rules from anything on [[Earth|Earth]].[^decaelo] This is the division that makes the system a physics of two worlds, and it is the division [[Isaac_Newton|Newton]] abolished by using one law of [[Gravity|gravitation]] for an apple and for the Moon. ### Terrestrial change Change in the sublunary world is the replacement of one form by another in a persisting substrate. Four kinds are distinguished: change of substance (generation and destruction), of quality (alteration), of quantity (growth and shrinking) and of place (locomotion). Locomotion is treated as the fundamental kind because the other three presuppose it. The framework survives, transformed, in the modern distinction between a [[State_of_matter|change of state]] and a [[Chemical_element|chemical]] change, and its vocabulary passed almost intact into [[Alchemy|alchemy]]. ### Natural place Each element has a place proper to it, arranged in concentric shells: earth at the centre, then water, then air, then fire. A body out of its place moves toward it and stops on arrival; a body in its place stays. Heaviness and lightness are not one quantity with two signs but two distinct tendencies, so fire rises *absolutely* rather than being pushed up. [[Archimedes|Archimedes]]' treatment of [[Buoyancy|buoyancy]] in the third century BC replaces the tendency with a balance of forces in a [[Hydrostatics|hydrostatic]] fluid, and it is the first quantitative correction to the scheme. ### Natural motion For a body falling in a medium Aristotle states two proportionalities: speed grows with the weight of the body and falls with the [[Density|density]] of the medium.[^phys-void] Written as one line, v = F/R, this is the equation the microsim runs against its modern replacement, m·dv/dt = m·g − k·v, whose closed-form solution from rest is v(t) = v_T·(1 − exp(−k·t/m)), with v_T = m·g/k and time constant τ = m/k = v_T/g.[^b032-linear] The reader has two controls: the medium's resistance k from 10⁻⁷ to 10³ kg/s on a log slider, and the body's mass. The plot shows v(t) against the dashed asymptote v_T, and a second dashed line for the vacuum case v = g·t. The lesson is in the time constant. At t = 2τ the body has reached 86.5 per cent of v_T, at t = 3τ 95.0 per cent (derived): after that, weight over resistance is the whole story and Aristotle's rule is exact. Take a 5 mm steel ball in honey, using Stokes' [[Laminar_flow|creeping-flow]] resistance k = 6πηr with η ≈ 10 Pa·s: k = 0.94 kg/s, m = 4.1 g, v_T = 4.2 cm/s and τ = 4.3 milliseconds, with a [[Reynolds_number|Reynolds number]] near 0.006 (all derived).[^b077-drag] The ball is on Aristotle's line before it has fallen a tenth of a millimetre. Slide k down toward air and τ stretches to seconds; slide it to zero and the asymptote disappears from the screen, because v_T = m·g/k diverges. Aristotle drew the same conclusion from the same formula and concluded that a void is impossible.[^phys-void] ### Unnatural motion Motion that is not toward a natural place is violent, and it requires a mover that acts continuously and in contact. This is the doctrine that fails most visibly, because an arrow keeps flying after the string stops pushing. Aristotle's answer, *antiperistasis*, has the displaced air close behind the arrow and drive it on — which makes the medium both the sole resistance and the sole propellant. [[John_Philoponus|John Philoponus]] attacked exactly this point in the sixth century, arguing that the thrower impresses an incorporeal motive power into the projectile itself and that the medium only retards it.[^philoponus] That impressed power, *impetus* to the Latin schoolmen, is the ancestor of [[Inertia|inertia]], and its caption in the microsim is Philoponus's objection in its original form: if the medium drives the arrow, then removing the medium should make the arrow fly better, not stop it. ### Continuum and vacuum Aristotle's rejection of the void is not stubbornness; it is an inference from his own law of motion, and the microsim reproduces the inference exactly. If speed is force divided by resistance, then as resistance tends to zero speed tends to infinity, and a body would traverse any distance in no time at all — which he takes to be absurd.[^phys-void] He argues in the same passage that a void could not explain why a body moves one way rather than another, since a void has no distinguishable places. Matter is therefore continuous and infinitely divisible, and there are no atoms and no empty gaps. The modern equation removes the paradox by changing what the force does. Force sets acceleration, not speed, so with k = 0 the solution is not infinite speed but v = g·t: unbounded in the limit t → ∞, perfectly finite at every moment. Aristotle had the right worry about the wrong equation. Torricelli's barometer of 1644 and the air-pump experiments that followed turned the question from a matter of principle into a matter of [[Pressure|pressure]], and a feather and a coin falling together in an evacuated tube became the standard demonstration that weight drops out of [[Free_fall|free fall]] entirely. ### Four causes To know a thing is to know its four causes: the material (what it is made of), the formal (what it is), the efficient (what brought it about) and the final (what it is for).[^phys-causes] Modern [[Causality_(physics)|physical explanation]] keeps the efficient cause, absorbs the formal and material causes into structure and composition, and rejects the final cause for inanimate bodies — a stone does not fall in order to reach the centre. The final cause survives in biology as function, and Aristotle's own use of it there is closer to modern practice than his use of it in physics. ### Biology Roughly a quarter of the surviving corpus is biological, and it is the strongest part. Aristotle describes the development of the chick embryo day by day, the chambered stomach of ruminants and the hectocotylus arm of the male octopus — the last dismissed as fable until it was confirmed in the nineteenth century.[^bio] The [[Biology|biological works]] show what his method could do when the subject rewarded patient description rather than measurement. ## Medieval commentary The physical works reached Latin Europe through Arabic transmission and commentary. Avicenna developed Philoponus's impressed power into *mayl*, an inclination that persists in the body; Averroes defended Aristotle's proportionality against Avempace's proposal that motion in a void would take a finite time. In the fourteenth century Jean Buridan gave impetus a quantitative form, proportional to the body's quantity of matter and its speed, and used it to explain both projectiles and the acceleration of falling bodies: the impetus accumulates as the body falls, so it goes faster the longer it has fallen.[^clagett] At Merton College the Oxford Calculators proved the mean speed theorem, that a uniformly accelerated body covers the same distance as a body moving steadily at its mean speed, and Nicole Oresme gave it a geometrical proof by area. These were not refutations of Aristotle so much as repairs, and they supplied the kinematic vocabulary — uniform difform motion, latitude of forms — that [[Galileo_Galilei|Galileo]] inherited ready-made. ## Life and death of Aristotelian physics The system held for nearly two thousand years because it explained the ordinary world well and had no quantitative rival. It died in stages. Copernicus removed the Earth from the centre, which dissolved the natural places; Galileo's [[Inclined_plane|inclined planes]] showed that fall is uniformly accelerated rather than uniformly fast, and his *Two New Sciences* of 1638 argued that bodies of different weight fall alike except for the medium's [[Drag_(physics)|resistance]];[^galileo] Torricelli produced the void; and Newton's *Principia* of 1687 replaced the whole apparatus with three laws and one inverse-square force acting at a distance, with no contact, no natural place and no distinction between the heavens and the Earth.[^newton] What remained of Aristotle in physics after 1687 was a vocabulary and a set of questions. ## Modern evaluations of Aristotle's physics The modern reading is not that Aristotle was careless but that he was describing a different regime. Carlo Rovelli has argued that Aristotelian physics is a correct approximate theory of the motion of bodies in fluids, with a definite domain of validity, and that v = F/R is a good law for a body at terminal velocity — which, in air or water, over the distances available to a Greek observer, is nearly every body nearly all the time.[^rovelli] The microsim's numbers support the reading: in honey the settling takes milliseconds, and a coin dropped 381 m through air reaches 18.1 m/s and stays there, arriving in 22.4 s instead of the 8.8 s it would take in vacuum — a 2.5-fold error, but a bounded one.[^b085-penny] Studies of untrained intuition find the same physics reappearing spontaneously in adults asked to predict trajectories, which suggests that the theory encodes a real regularity of the world we live in rather than a failure of reasoning.[^mccloskey] The honest summary is that Aristotelian physics is [[Viscosity|viscous]]-regime [[Fluid_mechanics|fluid mechanics]] without the fluid: it gets the steady state right and has no account of the transient. ## As listed in the Corpus Aristotelicum The physical treatises occupy a defined block of the corpus, cited by the page, column and line of Bekker's Berlin edition of 1831, which remains the standard reference for every modern translation.[^bekker] They are the *Physics* (184a–267b), *On the Heavens* (268a–313b), *On Generation and Corruption* (314a–338b) and the *Meteorology* (338a–390b), followed by *On the Soul* and the short treatises of the *Parva Naturalia*, and then by the biological works — *History of Animals*, *Parts of Animals*, *Movement of Animals*, *Progression of Animals* and *Generation of Animals*. Several works transmitted under Aristotle's name, notably the *Mechanical Problems* and *On the Universe*, are now judged to be by later members of his school; the *Mechanical Problems* is nonetheless the earliest surviving treatment of the lever and the balance. ## See also - [[Terminal_velocity]] - [[Free_fall]] - [[Buoyancy]] - [[Hydrostatics]] - [[Aristotle]] - [[John_Philoponus]] - [[Natural_philosophy]] ## Notes - *Natural place* and *natural motion* are not two doctrines but one: the place is defined by where the element goes, and the motion is defined by the place it seeks. The circularity is deliberate and was recognised in antiquity. - The resistance constant k in the microsim is the coefficient of a linear (Stokes) drag law, appropriate to small, slow bodies. Large, fast bodies in air follow a quadratic law, and the falling-coin figures quoted under *Modern evaluations* come from that law, not from the sim's. - Footnote definitions for this page are collected under *References*. ## References [^phys-void]: Aristotle. *Physics*, Book IV, chapters 6–9 (215a–216a): speed varies with the weight of the moving body and inversely with the density of the medium, whence the argument that motion in a void would be instantaneous and a void therefore impossible. Cited by Bekker page; see [^bekker]. [^phys-causes]: Aristotle. *Physics*, Book II, chapter 3 (194b–195a), and *Metaphysics*, Book V, chapter 2: the material, formal, efficient and final causes. [^decaelo]: Aristotle. *On the Heavens*, Book I, chapters 2–3 (the fifth body and its natural circular motion) and Book IV (heaviness and lightness as distinct tendencies). [^gencorr]: Aristotle. *On Generation and Corruption*, Book II, chapter 3: the four sublunary elements derived from the contrarieties hot/cold and wet/dry. [^bio]: Aristotle. *History of Animals*, *Parts of Animals* and *Generation of Animals* (the chick embryo, the ruminant stomach and the hectocotylus of the male octopus). [^bekker]: Bekker, Immanuel, ed. (1831). *Aristotelis Opera*. Berlin: Georg Reimer. The source of the standard page–column–line citations (184a–390b for the physical treatises) used in every modern edition. [^b032-linear]: Trench, William F. (2013). *Elementary Differential Equations with Boundary Value Problems*. Section 4.3, "Elementary Mechanics", pp. 160–162 (linear-drag equation m·v′ = −m·g − k·v, its exponential solution and the terminal velocity v_T = m·g/k; g taken as 9.8 m/s²). Portal Book 032. https://open.umn.edu/opentextbooks/textbooks/elementary-differential-equations-with-boundary-value-problems [^b085-penny]: Downey, Allen B. (2021). *Physical Modeling in MATLAB*, version 4.0. Chapter 12, pp. 125–131 (a 2.5 g coin dropped 381 m: 8.8179 s and 86.4 m/s with no air; 22.4 s and 18.1 m/s with quadratic drag at b = 7.5×10⁻⁵ kg/m, for which √(m·g/b) = 18.07 m/s). Portal Book 085. https://open.umn.edu/opentextbooks/textbooks/physical-modeling-in-matlab [^b077-drag]: Ling, Samuel J.; Sanny, Jeff; Moebs, William (2016). *University Physics Volume 1*. OpenStax. Chapter 6, "Applications of Newton's Laws", pp. 297–304 (drag; the quadratic law is used for large, fast bodies and Stokes' linear law F = 6πrηv for small, slow ones; skydiver speeds of roughly 350 km/h head-first and 200 km/h spread-eagle). Portal Book 077. The displayed drag equations on these pages were lost in text extraction and the standard forms F_D = ½CρAv², v_T = √(2mg/(ρCA)) and F_s = 6πrηv are quoted here as standard forms, to be verified against the PDF pages (page to pin). [^philoponus]: Sorabji, Richard, ed. (1987). *Philoponus and the Rejection of Aristotelian Science*. London: Duckworth (Philoponus's impressed motive power, his denial of *antiperistasis*, and his claim that bodies of different weight dropped together arrive almost together; page to pin). [^clagett]: Clagett, Marshall (1959). *The Science of Mechanics in the Middle Ages*. Madison: University of Wisconsin Press (Avicenna's *mayl*, the Avempace–Averroes dispute over motion in a void, Buridan's impetus, the Merton mean speed theorem and Oresme's geometrical proof; page to pin). [^galileo]: Galilei, Galileo (1638). *Discorsi e dimostrazioni matematiche intorno a due nuove scienze*. Leiden: Elzevir. Third Day, on naturally accelerated motion (page to pin). [^newton]: Newton, Isaac (1687). *Philosophiæ Naturalis Principia Mathematica*. London: Royal Society. Book I, the axioms or laws of motion, and Book III, the system of the world (page to pin). [^rovelli]: Rovelli, Carlo (2015). "Aristotle's Physics: A Physical Theory of Fluid Bodies." *Journal of the American Philosophical Association* 1 (1) (pages to pin). [^mccloskey]: McCloskey, Michael (1983). "Intuitive physics." *Scientific American* 248 (4) (pages to pin). ## Sources - Aristotle, *Physics*, *On the Heavens*, *On Generation and Corruption* and *Meteorology*, cited by Bekker page from Bekker (1831). - Trench (2013), *Elementary Differential Equations with Boundary Value Problems*, §4.3 "Elementary Mechanics", pp. 160–170. Portal Book 032. - Downey (2021), *Physical Modeling in MATLAB* 4.0, chapters 11–12, pp. 99–134. Portal Book 085. - Ling, Sanny and Moebs (2016), *University Physics Volume 1*, chapter 6 "Applications of Newton's Laws", pp. 261–322. Portal Book 077. ## Further reading - Sorabji, Richard, ed. (1987). *Philoponus and the Rejection of Aristotelian Science*. The standard collection on the first sustained attack from inside the tradition. - Clagett, Marshall (1959). *The Science of Mechanics in the Middle Ages*. The medieval kinematics that Galileo inherited. - Rovelli, Carlo (2015). "Aristotle's Physics: A Physical Theory of Fluid Bodies." 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